We constructed hydrodynamical model atmospheres for mid M-type main- , as well as pre-main-sequence objects .
Despite the complex chemistry encountered in such cool atmospheres a reasonably accurate representation of the radiative transfer is possible .
The detailed treatment of the interplay between radiation and convection in the hydrodynamical models allows to study processes usually not accessible within the framework conventional model atmospheres .
In particular , we determined the efficiency of the convective energy transport , and the efficiency of mixing by convective overshoot .
The convective transport efficiency expressed in terms of an equivalent mixing-length parameter amounts to values around \approx 2 in the optically thick , and \approx 2.8 in the optically thin regime .
The thermal structure of the formally convectively stable layers is little affected by convective overshoot and wave heating , i.e .
stays close to radiative equilibrium .
Mixing by convective overshoot shows an exponential decline with geometrical distance from the Schwarzschild stability boundary .
The scale height of the decline varies with gravitational acceleration roughly as g ^ { - \frac { 1 } { 2 } } , with 0.5 pressure scale heights at \log \mathrm { g } =5.0 .